Sam Loyd's Archery Puzzle

The Puzzle:

Sam Loyd's Archery Puzzle
Here is an odd little puzzle which occurred the other day at an archery meeting.

The young lady who carried off the first prize scored exactly one hundred points.

The scores on the target are: 16, 17, 23, 24, 39 and 40.

Can you figure out how many arrows she must have used to accomplish the feat?
Do you have the answer? Check against our solution!